Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #27132567 | C2 | semidirect |
| 3. #27132554 | C2 | semidirect |
| 4. #27132553 | C2 | semidirect |
| 6. #27132534 | C2 | semidirect |
| 7. #27132531 | C2 | semidirect |
| 8. C4×(C2×D191)⋊C4 | C2 | semidirect |
| 9. C4×C4⋊C4×C191 | C2 | semidirect |
| 13. #20259310 | C4 | semidirect |
| 34. C2×Dic382 | C2×C4 | semidirect |
| 47. (C2×D191)⋊C4 | C2×C4 | semidirect |
| 48. (C2×D191)⋊C4 | C2×C4 | semidirect |
| 58. C42×C191 | C2×C4 | semidirect |
| 118. C191 | #2337 | semidirect |
| 127. C4×C4⋊C4 | D191 | semidirect |
| 177. C42 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259310 | 2 |
| #27132567 | 2 |
| #27132554 | 2 |
| #27132553 | 2 |
| #27132541 | 2 |
| #27132534 | 2 |
| #27132531 | 2 |
| C4×(C2×D191)⋊C4 | 2 |
| C4×C4⋊C4×C191 | 2 |
| #2337 | 191 |